Take a look at the bitscope. I believe it started out as a build-it-yourself scope, and they made schematics and such available. It's now a commercial product but I believe the schematics for the old version are still available. At least you can get an idea of what's involved.
It sounds like you're hoping to hook an ADC to some USB board and just send all the data to the PC in real-time and do all the processing there. Bear in mind the kind of data rate you're dealing with here. If you want to build a 10MHz scope, you need to sample each channel at at LEAST twice that, so you're looking at a minimum of 20Ms/s per channel. If you're using 8-bit ADC's that's 320 Mbps, which is not all that far from the usb 2.0 limit of 480Mbps, and is likely much more than you could possibly achieve with some kind of commercial USB board... and would likely be far too challenging for a school project.
Normal digital scopes capture data intermittently to high-speed RAM, and the data can then be transferred to a PC (or displayed on a screen, or whatever) at a more reasonable speed. I believe the bitscope has an FPGA which handles the high-speed interface between ADC's and RAM, and a microcontroller for the lower-speed PC interface.
Starting from zero and learning to use FPGA's, microcontrollers, and high-speed ADC's and RAM, along with all the other design challenges, seems like a VERY tall order for a school project. Making an oscilloscope that works somewhere in the range of tens or hundreds of KHz might be reasonable, but 10MHz is a different story, and I find it surprising that any advisor would approve such a project...